Parallel and Perpendicular Lines

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Section 3.3

• Parallel and Perpendicular Lines

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Parallel Lines

• What does it mean for lines to be parallel?
• They dont intersect, ever.
• They have the same slope, ie, the same rate of
  change.
• Theres a geometrical argument as well, involving
  congruent angles.
• Officially
• Two non-vertical lines are parallel if they meet
  both these conditions
• Their slopes are equal
• They have different y-intercepts.
• Vertical lines are always parallel to each other.

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Example Graph
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Example- are they parallel?

• Line 1 -2x3y 8
• Line 2 4x-6y 12

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Perpendicular Lines

• What are perpendicular lines?
• Lines that intersect at right angles (90 deg.)
• What about their slopes?
• We define two nonvertical lines to be
  perpendicular if and only if their slopes
  multiply to be -1.
• In other words, their slopes must be negative
  reciprocals.
• Any vertical line is perpendicular to any
  horizontal line.

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Parallel, Perpendicular Slope Summary

• Let
• Line 1 have slope m1
• Line 2 have slope m2
• Then
• If m1 m2, the lines are parallel
• If or , the lines are perpendicular.

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Parallel, Perpendicular, or neither?

• a)
• b)
• c)
• d) Line 1 contains (-2,3) and (4,-9)
• Line 2 contains (-3,-6) and (1,-4)

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Finding the equation of a parallel or
perpendicular line

• Note To find the equation of a line, the slope
  MUST be either given, or calculated.
• Step 1 Find slope of the given line (put into
  slope-intercept form)
• Step 2 Determine slope of new line (either same
  as given line, or negative reciprocal)
• Step 3 Use point-slope form with given point to
  find equation!

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More Examples.

• Find the equation, in slope-intercept form, of
  each line
• a) Parallel to y -3x 2, through the point
  (5,-1)
• b) Parallel to 12x 10y 5, through the pt
  (-15,0)
• c) Perpendicular to , through the pt (10,2)
• d) Perpendicular to 7x 2y6, through the pt
  (0,-3)